The 24-year-old midfielder came off in Leicester's 1-0 win over Norwich and is set to miss Leicester's game against West Brom and Watford.
The Foxes are two points clear at the top of the Barclays Premier League and host the Baggies on Tuesday.
Andy King is expected to replace him but boss Claudio Ranieri feels Kante will not return before they head to Watford on Saturday
He said: " We lose him for the next two matches. I hope only two. It's a little painful, he suffered during all of the season and now we want to give him some rest. Two matches and he can restart.
"All the season he had a problem with the other leg and now this time the new leg
Maybe he made a compensation and charged too much on the other leg.
"He has been extraordinary but I am very confident because we played King and he has started very well. I am very confident with him.
"Let me now play and then I will tell you what I will lose (from Kante). N'Golo recovers a lot of balls but not only this, he starts the counter-attack. I am very confident Drinky (Danny Drinkwater) and Kingy could be the same, they are doing very well."
Kante has featured in every league game for the Foxes this season, making 30 appearances and scoring once in November's 2-1 win over Watford.
Source: PA